Nonlinearity continuation method for steady-state groundwater flow modeling in variably saturated conditions

First-order continuation method for steady-state variably saturated groundwater flow modeling

Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has been applied to date having a trivial, zeroth-order predictor. In this article, effect of a more sophisticated predictor technique is examined. Numerical experiments are performed with finite volume and mimetic finite difference discretizations on various problems, including real-life examples.

Comparison of nonlinear solvers within continuation method for steady-state variably saturated groundwater flow modeling

Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search algorithm was used to solve the intermediate problems. In this paper, other solvers such as Picard and mixed Picard-Newton methods are considered, combined with slightly modified line search approach. Numerical experiments are performed with advanced finite volume discretizations on model and real-life problems.

An efficient numerical scheme for fully coupled flow and reactive transport in variably saturated porous media including dynamic capillary effects

In this paper, we study a model for the transport of an external component, e.g., a surfactant, in variably saturated porous media. We discretize the model in time and space by combining a backward Euler method with the linear Galerkin finite elements. The Newton method and the L-Scheme are employed for the linearization and the performance of these schemes is studied numerically. A special focus is set on the effects of dynamic capillarity on the transport equation.

变饱和多孔介质中Richards方程的高效求解器

An Efficient Solver for the Richards Equation for Variably Saturated Flows in Porous Media

针对强非线性水力传导率和水分保持关系的Richards方程，提出基于非线性Gauss-Seidel光滑子的多重网格求解器，通过扩散算子的三角分裂和对角稳定化实现高效鲁棒求解。

用于模拟非饱和多孔介质中动力失效与断裂的计算耦合大变形近场孔隙力学

Computational coupled large-deformation periporomechanics for dynamic failure and fracturing in variably saturated porous media

该研究构建了考虑被动气压的耦合大变形近场孔隙力学范式，引入混合界面材料点模拟饱和状态转变，结合更新拉格朗日-欧拉框架与隐式无网格方法，实现非饱和多孔介质动力失效与断裂的高精度数值模拟。

Adaptive modelling of variably saturated seepage problems

In this article we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a nonlinear Darcy-Buckingham law with physical constraints on subsurface-atmosphere boundaries. This leads to the formulation of the problem as a variational inequality. The solutions to this problem are investigated using an adaptive finite element method based on a dual-weighted a posteriori error estimate, derived with the aim of reducing error in a specific targ…